Solve tan(45)+sqrt{2}cos(45)

$$\tan ( 45 ) + \sqrt{ 2 } \cos ( 45 )$$

Evaluate

$$2$$

Short Solution Steps

Get the value of \tan(45) from trigonometric values table.

$$1+\sqrt{2}\cos(45)$$

Get the value of \cos(45) from trigonometric values table.

$$1+\sqrt{2}\times \frac{\sqrt{2}}{2}$$

Express \sqrt{2}\times \frac{\sqrt{2}}{2} as a single fraction.

$$1+\frac{\sqrt{2}\sqrt{2}}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{2}{2}.

$$\frac{2}{2}+\frac{\sqrt{2}\sqrt{2}}{2}$$

Since \frac{2}{2} and \frac{\sqrt{2}\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{2+\sqrt{2}\sqrt{2}}{2}$$

Do the multiplications in 2+\sqrt{2}\sqrt{2}.

$$\frac{2+2}{2}$$

Do the calculations in 2+2.

$$\frac{4}{2}$$

Divide 4 by 2 to get 2.

$$2$$